# Joined Common Chords of Napoleon's Circumcircles

29 July 2013, Created with GeoGebra

### An Equilateral Triangle in Napoleon's Circumcircles

Let $ABC',$ $BCA',$ and $CAB'$ be Napoleon's triangles constructed on the sides of $\Delta ABC.$ Choose point $D$ on the circumcircle $ABC',$ pass it through $A$ to the intersection $F$ with $C(CAB')$ and through $E$ to the intersection $E$ with $C(BCA').$

Triangles $DEF$ is equilateral.

### Hint

The problem is very simple; it submits to chasing inscribed angles.

### Solution

The solution is outlined in an old variant of this problem.

### Acknowledgment

The problem described on this page stems from an observation of Hirotaka Ebisui.